Neural Network Predictive Control for Improved Reliability of Grid-Tied DFIG-Based Wind Energy System under the Three-Phase Fault Condition

Abstract

This research explores a distinctive control methodology based on using an artificial neural predictive control network to augment the electrical power quality of the injection from a wind-driven turbine energy system, engaging a Doubly Fed Induction Generator (DFIG) into the grid. Because of this, the article focuses primarily on the grid-integrated wind turbine generation’s dependability and capacity to withstand disruptions brought on by three-phase circuit grid failures without disconnecting from the grid. The loading of the grid-integrated power inverter causes torque and power ripples in the DFIG, which feeds poor power quality into the power system. Additionally, the DC bus connection of the DFIG’s back-to-back converters transmits these ripples, which causes heat loss and distortion of the DFIG’s phase current. The authors developed a torque and power content ripple suppression mechanism based on an NNPC to improve the performance of a wind-driven turbine system under uncertainty. Through the DC bus linkage, it prevented ripples from being transmitted. The collected results are evaluated and compared to the existing control system to show the advancement made by the suggested control approach. The efficacy of the recommended control methodology for the under-investigation DFIG system is demonstrated through modelling and simulation using the MATLAB Simulink tool. The most effective control technique employed in this study’s simulations to check the accuracy of the suggested control methodology was the NNPC.

1. Introduction

According to the global energy statistics for 2021, there will be a constant growth in the need for electricity along Social, Technological, and Environmental Pathways (STEPs), making coal-generated power almost useless globally [1]. Modern times have seen a lot of discussion about wind energy due to its prospective ability to condense greenhouse gas releases. Its lower carbon impression has improved its profile in modern times, making it an imperative renewable energy source. However, wind energy systems’ ambiguity, intermittency, and unpredictability make their connection to the grid problematic. Consequently, there is a requirement for effective control methodologies that may enhance wind energy systems’ performance and expedite their incorporation into the grid. Wind energy systems have employed neural network predictive control (NNPC) as an effective control methodology. Using neural network modelling, the model-based control method known as NNPC predicts the system’s futuristic nature and engenders control activities following that forecast. The capacity to accomplish uncertainties and nonlinearities, its low computing cost, and its capability to handle restrictions are only a few of the advantages that NNPC puts forward over more conventional control methodologies, such as PI and model predictive control [2,3,4,5,6].

Neural network predictive control methodology is a superior approach that improves the effectiveness of wind energy systems tied to the grid [2,7]. NNPC aims to achieve a stable grid link, enhance the wind-driven turbine’s productivity, and ensure that it operates as effectively as is feasible [6]. The basis of NNPC is the concept of neural networks, which simulate the operation of the human brain by applying a network of associated inputs and outputs [5]. The system can constantly evaluate and predict the operation of the wind-driven turbine by utilising NNPC, which allows it to make essential system alterations on a real-time basis. To efficiently attach and deactivate the turbine, NNPC can also manage the grid connection [2]. Several advantages come with using NNPC, such as better grid stability, reduced operational costs, and improved energy efficiency. This study’s main objective is to examine how NNPC can improve wind energy schemes linked to improving the grid. The designing part of a suitable neural network prototype for wind energy systems and the building and application of an NNPC controller for wind energy systems were the other two major themes of this paper’s emphasis on NNPC for wind energy systems. The evaluated literature covers a wide range of DFIG-integrated wind energy control system (WECS) strategies, the benefits of which have been emphasised elsewhere (increased effectiveness, power excellence, frequency support to the grid, power smoothing, etc.). Direct Torque Control (DTC) [8,9,10,11], Direct Power Control (DPC) [12,13,14], and their developed versions throughout time are the most often used control methods, along with Vector Control (VC) [15,16,17,18] or Field-Oriented Control (FOC) [15,19], respectively. Due to the instability within the wide operating range caused by many cascade control loops and improper decoupling of the d-q axis variables, these control techniques have problems with signal generation by PI controllers and slower response times for the required changes [20].

Similarly, the DTC have the disadvantages of high rippling torque and poor transient behaviour [21]. However, the study [22,23] suggested the DPC of the DFIG-grounded wind energy control system adjusts the active and reactive power by using the rotor flux and stator flux influences. The DPC control methodology acts as a mitigation approach to overcome the DTC control shortcomings and ultimately enhance the grid’s power quality. However, the DPC control has drawbacks, namely, substantial power loss in the converter’s switching architecture.

The conventional control system challenges and the merits of ANN motivated us to develop a novel design based on ANN control strategy for improved grid-tied DFIG energy system performance. The machine learning predictive (MLP) [22,23,24,25] neural network controller engages in abolishing the need for PI/PD/PID parameters’ design and further reduces the convolution of the regulator structure to enhance active and reactive power regulation without the application of PI/PD/PID or a matrix table for the switch over functions [26]. A proportional study linking an ANN-based PI controller and a standard one in [27] summarises the benefits and imperfections of both regulators while applying them in the DFIG system in adaptable load conditions. A probabilistic fuzzy neural network controller design study in [28,29] describes the control of active and reactive power of the DFIG as a reference to maintain the grid support. The study signifies the improved execution of the suggested approach; however, the rules are endorsed only for smaller systems.

This research article proposes an NNPC-based control solution to the rippling torque and power smoothing problems associated with a DFIG-grounded wind energy control technique. The proposed NNPC-based DPC methodology controls the DC-bus link and provides frequency to the grid to achieve the earlier objectives. The results are contrasted with a DPC system based on PI/PD/PID controllers to assess the effectiveness. The Rotor Side Converter (RSC) and Grid Side Converter (GSC) blocks act as power converters in the grid interfaced WECS. To turn the three-phase measure into a synchronous reference frame, the d and q values may be used independently. Hence, the RSA and GSC blocks employ the dq to abc or abc to dq blocks. The Phase-Locked Loop (PLL) block synchronises the conversions with the applicable voltage reference and angle. The power converters’ gate-switching pulses use space vector modulation generated using the SVM block.

The sections of the document are as follows: In Section 2, the authors provide a synopsis of the NNPC’s design, which is required for this inquiry. For the DFIG-grounded wind energy control techniques, mathematical modelling and the creation of the recommended control methods are presented in Section 3. The authors support their study’s findings in Section 4 and evaluate them using a reasonable framework lens. The study’s findings are then summarised, with Section 5 focusing on the most crucial conclusions.

2. Literature Review

The doubly fed induction generator connected to the power grid has been widely used in the wind-driven turbine energy conversion system. It reaped benefits on independent active and reactive power regulation because of its variable speed and constant frequency characteristics [24,25]. When the stator is connected directly to the grid, the DFIG is vulnerable to grid failures, significantly when the voltage decreases, causing voltage sag and the stator current changes [26,27]. The stator of grid-tied DFIGs is directly connected to the grid using grid-side converters (GSCs), which control dc-link voltage [24]. In contrast, rotor side converters (RSCs) regulate generator speed and reactive power [25].

In [26], the authors discussed how separating the positive and negative sequence currents and reducing second harmonic current distortions improve voltage dips to a certain level, preventing the DFIG from being disconnected from the grid to protect the rotor side converter and further strengthening voltage dip impact on the stable grid’s operation. Hardware solutions, such as crowbar equivalent circuits [27], static compensators (STATCOMs) [28,29], and dynamic voltage restorers (DVRs) [30] are used to partially solve low voltage ride through (LVRT) problems.

Modern grid codes require wind turbines (WTs) to stay connected to the grid during transient and severe faults following a technical requirement called LVRT. This provides millisecond-reactive support to maintain the stability of the power grid [31].

The researchers suggested a standard solution for the dynamic behaviour and ride-through capability of DFIG-based wind turbines under grid faults in [28,29,32] by supplying a short circuit to the rotor windings by enabling the crowbar [27,33] and then disconnecting the turbine from the grid to achieve the LVRT operation of wind turbines. However, the crowbar circuit must be enabled throughout the dip due to a sustained rotor over-current caused by three-phase fault voltage dips [27]. When the crowbar circuit is enabled, the DFIG absorbs large amounts of reactive power from the grid, which is not conducive to grid recovery.

To improve the capabilities of LVRT for DFIGs with significant voltage dips, the researcher presented an improved, mixed proportional resonant current control approach for RSC [34]. The central PR controller does not need numerous frame transformations and can compensate for the stated harmonic currents in the suggested control strategy, which has the advantage of a quick dynamic reaction. The auxiliary PR controller adjusts the RSC output voltage to reduce rotor fault currents without extracting the dc and stator flux’s negative sequence components.

In contrast, a new simplified hardware approach utilising fault current limiters (FCL) is presented in [35] to limit the short circuit current in the rotor to an acceptable value using grid compliance regulation. In addition, it maintains the DFIG’s connection to the power grid in the event of symmetrical faults. The superconducting fault current limiter (SFCL) coil, during a severe three-phase-to-ground (3LG) fault, limit the rotor overcurrent [36]. A resistive type SFCL coupled in series with the rotor has been investigated for rotor overcurrent protection in grid-integrated DFIGs [36]. This resistive-type SFCL uses a lot of electricity on the rotor side. However, the heat induced in SFCL requires tens of kWh for cooling. Nevertheless, three-phase grid faults also cause a large transient overcurrent in the stator and rotor windings, and overvoltage in the DC link voltage [26]. Subsequently, FCL approaches are applied at different locations, increasing the cost and power quality problems.

Researchers have divided grid failures into two groups in the literature to steadily analyse DFIGs during voltage unbalance [37,38]. The classic PI controller receives feedback from the measured torque and reactive power pulsation to create a rotor compensation voltage used to regulate the rotor’s positive and negative sequence currents based on positive and negative reference frames. To eliminate the delay brought on by the positive and negative sequence decomposition of the rotor current, the researchers presented a simplified version of the added-on resonance-based controller to the conventional PI controller [39].

Then, in [40], the authors suggested using a proportional current control with a first-order low-pass filter disturbance observer (DOb) to independently control both the positive and negative sequence current components under asymmetric grid voltage conditions. The researchers described a model predictive control methodology in [41] that uses the input–output feedback linearisation method, a useful linearised technique.

With three-phase or symmetrical failures, overcurrent and overvoltage are produced in the power converter at the RSC and the DC bus capacitor, respectively. The RSC’s semiconductor switches could be harmed, causing the DFIG to shut down. Rotor currents determine the load on the power converter during failures; hence, they must be less than 2.0 pu to preserve the RSC switches. The researchers proposed distinctive LVRT approaches [42], which comprise distinct advantages and disadvantages. Considering that the back-to-back converter is particularly sensitive to grid disturbances, the researchers have been focusing on the significant effort that has been recently devoted to ensuring the reliable operation of power semiconductors owing to high costs and extended maintenance periods after failures [37]. Notably, the thermal profile is an essential indicator of the lifetime of semiconductors, with significant influence on reliable system operation [38,39,40]. The number of energy cycles and the average junction temperature are fundamental aspects that do affect the junction temperature fluctuation [41].

The synchronisation process, which is primarily in charge of managing Renewable Energy Sources (RESs), must quickly and precisely control the voltage state of the grid (such as phase, frequency, and amplitude). The grid voltage is usually detected using PLL synchronisation methodology. The design and functionality of PLL directly influence the dynamics of the RES’s grid-side converter. The authors examined modern PLL-based synchronisation algorithms regarding their characteristics, design principles, and features in settings with normal, aberrant, and harmonically disturbed grids [40]. The authors provided reasonable benchmarking and selective guidelines after tentative assessments of the selected PLL processes in numerous grid circumstances.

The research scholars suggested a Model Reference Adaptive Control (MRAC) of Static Synchronous Compensator (STATCOM) in [43] to advance the incorporation of wind-driven turbine-based Self-Excited Induction Generators (SEIGs) into electrical grids. According to the study, the authors generated a grid-tied SEIG’s reactive power stream using an adaptive MRAC system created at the Massachusetts Institute of Technology. The authors adapted the Generic Algorithm (GA) parameters for voltage, currents, and wind generator speed feedback. The outcomes show that the suggested adaptive control performance is more active and consistent than a static PI controller. The unusual operating conditions in WECSs are dominated by utilising the voltage-source power inverter sinusoidal pulse width modulation of the STATCOM. This results in increased system ability for the Low-Voltage Ride-Through (LVRT).

The authors researched the LVRT of grid-connected DFIG-based wind turbines [44]. The study proposed a detailed analysis backed by a computerised simulation of the active and transient behaviours of DFIGs under symmetrical and asymmetrical grid voltage sags using a novel rotor side control strategy. The suggested control technique enlightened the DFIG’s reliability concerns while concentrating on reducing the rotor side voltage and current shock under unexpected grid circumstances.

The research article [45] offered a multiple-objective prognostic energy management method centred on machine learning technology for a RES grid system. The researchers included three stages of control systems in the suggested strategy: a two-fold prediction modelling for energy production based on enduring causal widened convolutional networks and electrical load on the system, as well as a logical level to regulate the computational load and correctness, and a multiple-objective optimisation for effective energy trading with the power grid using a battery charge arrangement. The prediction modelling employed in this work is implemented on a typical computational model to offer a one-step forward forecast of the RES’s output and load utilising a sliding window training approach.

The authors suggested a “Micro-grid Key Elements Model” (MKEM) in [46], setting up prominence on intelligent micro-grid systems that include both a primary grid and several embedded micro-grids. The recommended grid architecture’s virtualisation attempts are challenged by Photovoltaic (PV) penetration, back sustaining, and unpredictable supply. The simulation effects demonstrate the influence of Renewable Energy (RE) integration into the grid and emphasise the batteries’ functionality in supporting system stability.

The research analysts suggested a Dynamic Voltage Restorer (DVR) controller using an Artificial Neural Network (ANN) and HOMER software tool to boost a stand-alone mixed renewable energy system’s effectiveness in supplying a novel town [47]. The booster converters, one for each energy source, integrate the RES sources into a single DC connection. A DC/AC DVR converter then connects and controls the shared DC connection to the load side of the AC in various typical working situations.

The authors in [48] tried to label Small and Medium Enterprises (SMEs) knowledge and its prospective to be controlled to ease the WECS’s-tied power grid stability. With the WECS’s integrated power system, SMEs might be installed at the wind generator terminal, the conversion system, or the tie-line PCC to reduce the power jerks and enhance the LVRT. The SMEs’ capacity varies greatly amongst research articles on related applications. At the 1.5 Mega Watt and 3 Mega Watt PMSG-based WECS conversion systems, 0.45 GJ and 2.577 Mega Joules SMEs are connected. The wind speed pattern of the first study required lengthy (20-min) periods of SMEs’ discharge, but the later study needed to alternate charging and discharging for just brief intervals (less than 20 min).

The researchers evaluated the model using HOMER (Hybrid Optimization Model for Electric Renewable) software in terms of the Net Present Cost (NPC) and Cost of Energy (COE) to address the suburban and farming electrical load needs of an energy-deprived civic centre. The research analysts in [48] suggested the most cost-effective achievable solution, including three potential ideal arrangements—PV/battery, wind/battery, and wind/PV/battery, for economic analysis and optimal scaling. The study is yet to conclude the design and the ideal component sizes for the most cost-effective configuration.

The research study in [49] proposed a progressed Virtual Synchronous Generator (VSG) control methodology based on fuzzy logic. The researchers introduced a fuzzy rule system that dynamically adjusts the droop coefficient and frequency compensation in absolute time. This methodology allows distributed generation to distribute power output in a stable approach following its capability. Results from simulations and experiments indicate that the suggested system realises a real-time interface between the fuzzy logic set of rules and the VSG control element. This methodology can significantly increase the power distribution precision whilst maintaining the bus voltage and system’s frequency stability and effectively advance the dynamic execution and steadiness of the plan.

The research scholars offered a thorough state-of-the-art assessment of the grid-tied distributed generators’ (DGs) control methodologies [50]. The earlier distributed review lessons distinctly evaluate each DG and lack a logical argument on the control methods deprived of appropriate classification. Hence, it is stimulating to assess each control method’s improved proportional performance and understand the control method’s need for all DGs. This article first exclusively describes the comprehensive control arrangements for DGs as Control Blocks (CBs). Second, the CBs are used to categorise each DG’s available modern control approaches. Lastly, each CB is sensibly studied considering the control process essential for the DG’s element and the best modern control schemes recommended.

The research scholars analysed articles on the DFIG’s advanced and conventional control systems in [3,4,51,52]. They concluded that the AI methodologies have a better advantage over the conventional control system and have a superior strategy that boosts the efficiency of wind energy systems connected to the grid. In conjunction with the studied AI methodologies, the researchers analysed that the metaheuristic method is a high-end process to discover, create, or select a fractional search algorithm that may deliver an adequate solution to an optimisation challenge, expressly with partial or restricted computation ability. The formulation of the optimisation task of a particular application optimises the result managed using a linear or nonlinear encoding methodology.

The metaheuristic methodologies are classified as population-based methodologies such as GA, Particle Swarm Optimization (PSO) [53], and differential evolution [54]. Associated with the trajectory-based procedures, they are greater at meeting the speed and the overall penetrating competency and are exclusively beneficial for numerous optimisation assignments. Due to massive benefits, population-based methodologies have resolved most of the reform assignments in power electronic converters [55]. Metaheuristic algorithms have turned out to be smart because of their distinct benefits over customary algorithms. Since metaheuristic methods with some hybrid techniques can resolve multiple-objective multiple-solution and nonlinear designs, they are involved in determining higher-quality resolutions to an ever-growing quantity of complex problems, such as the amalgamation of novel predictive control systems.

Table 1. The applications of metaheuristic methods in a power electronics’ control system.

Methods	Type	Conventional Algorithms	Applications	Advantages and Drawbacks
			Control Systems	Parallel Ability	Global Union	Implementation Ease	Merge Speed
Metaheuristic	Population-based methods	Particle Swarm Optimisation (PSO)		Yes	BEST	GOOD	GOOD
		Crow Search Algorithm (CSA)			BETTER	BETTER	BETTER
		Ant Colony Optimisation (ACO)			BETTER	BETTER	BETTER
		Differential Evolutionary (DE)			BETTER	BETTER	BETTER
		Immune Algorithm (IA)			BETTER	BETTER	BETTER
		Genetic Algorithm (GA)			BEST	GOOD	GOOD
	Solutions with AI applications: 1. Accomplishes pre-training with an appealing smaller learning rate to accomplish faster merging.
	Trajectory-based methods	Tabu Search Method (TSM)	Control System	No	GOOD	BEST	BEST
		Simulated Annealing Method (SAM)			BETTER	BEST	BEST
	Solutions with AI applications: 1. Works on undefined jump location. 2. Less inclined to impulsive merging. 3. Least possible to become caught in localised targets.

indicates the applications of the metaheuristic method’s superiority.

Table 2. A comparative approach in terms of distinct issues of reviewed control strategies.

Dynamic Performance Measures	PI Control	Fuzzy Logic Control	Machine/Deep Learning				Reinforcement Learning
			FFNN	NN/FNN	RNN	RFNN
Dataset requirement	Not applicable	Superior	Finest	Superior	Good	Good	Not applicable
Approximation ability	Good	Good	Superior	Finest	Finest	Finest	Finest
Robust/Strength	Good	Better	Good	Superior	Superior	Finest	Finest
Calculation burden	Good	Finest	Finest	Superior	Good	Good	Not applicable
Expert knowledge rooted in the ability	Yes	Yes	No	Yes	No	Yes	No
Rise time	Less	More	Good	Superior	Superior	Finest	Finest
Transients	Present	Not present	Not present	Not present	Not present	Not present	Not present
Overshooting	More	Less	Very less	Smooth	Smooth	Smooth	Smooth
Simplicity	Moderate	Good	Superior	Finest	Finest	Finest	Finest
Variables	Numeric	Linguistic	Linguistic	Linguistic	Linguistic	Linguistic	Linguistic
Response time	Moderate	Good	Superior	Finest	Finest	Finest	Finest
System dynamics	Applicable	Not applicable	Not applicable	Not applicable	Applicable	Applicable	Applicable

shows the comparative metrics of control strategy approaches in terms of distinct issues, such as the response time and implementation complexity, strength, response time, burden calculations, expert knowledge, rise time, simplicity, variables, cost, approximation ability, overshooting, and system dynamics, among many other relevant dynamic performance measures.

3. Modelling and Controlling of DFIG

3.1. Power Control

The DFIG can be utilised to generate and supply electrical power at a constant frequency. Figure 1 [56] depicts a working induction machine basic theory of the interface between the stator side and rotor side magneto motive forces (MMF). The stator side winding currents initiate an MMF revolving at grid frequency, generating an MMF in the rotor side windings. The so-called slip frequency will spin this induced rotor MMF with the following value [30]: The rotor speed does not attain the stator side MMF.

$${\omega }_{slip}={\omega }_{mmf}^{rotor}={\omega }_{mmf}^{stator}-{\omega }_{rotor}$$

(1)

where ${\omega }_{slip}$ is the slip frequency, which corresponds to the rotor side current and voltage frequency, ${\omega }_{mmf}^{stator}$ is the stator frequency corresponding to the grid frequency in (rad/s), ${\omega }_{rotor}$ is the rotor side rotating frequency in (rad/s) corresponding to the product of the mechanical frequency and the number of magnetic pole sets.

Figure 2 [57] shows the DFIG’s corresponding circuit in the d-q frame of reference. It is possible to assume the electrical modelling of the DFIG in the d-q frame of reference. Here are the equations for the voltage, flux, and power of the rotor side and grid side converters for DFIG-based wind energy systems that may be expressed in the d-q frame of reference [58].

$$V_{ds}=R_s{I}_{ds}+\dot{{\phi }_{ds}}-{\omega }_s{\phi }_{qs}$$

(2)

$$V_{qs}=R_s{I}_{qs}+\dot{{\phi }_{qs}}-{\omega }_s{\phi }_{ds}$$

(3)

$$V_{dr}=R_r{I}_{dr}+\dot{{\phi }_{dr}}-{\omega }_r{\phi }_{qr}$$

(4)

$$V_{qr}=R_r{I}_{qr}+\dot{{\phi }_{qr}}-{\omega }_r{\phi }_{dr}$$

(5)

$${\phi }_{ds}=L_s{I}_{ds}+L_m{I}_{dr}$$

(6)

$${\phi }_{qs}=L_s{I}_{qs}+L_m{I}_{qr}$$

(7)

$${\phi }_{dr}=L_r{I}_{dr}+L_m{I}_{ds}$$

(8)

$${\phi }_{qr}=L_r{I}_{qr}+L_m{I}_{qs}$$

(9)

where $R_s$ and $R_r$ are the stator side and rotor side resistances, $L_s$ and $L_r$ are denoted as the stator side and rotor side winding’s self-inductance coefficient. $L_m$ is denoted as the mutual coupling coefficient between the stator side and rotor side. $V_{ds}$, $V_{qs}$, $I_{ds}$, $I_{qs}$, $V_{dr}$, $V_{qr}$, $I_{dr}$ and $I_{qr}$ are denoted as the stator side and rotor side voltage and current components in the d-q park reference frame [59]. The per-unit electromagnetic torque equation expressed in the d-q frame of park reference is assumed by [58]:

$$T_e={\phi }_{ds}{I}_{qs}-{\phi }_{qs}{I}_{ds}={\phi }_{qr}{I}_{dr}-{\phi }_{dr}{I}_{qr}=L_m\left(I_{qs}{I}_{dr}-I_{ds}{I}_{qr}\right)$$

(10)

Considering only the resistances in the stator side and rotor side, the reactive and active stator powers of the DFIG are [58]:

$$P_s=\left(\frac{3}{2}\right)\left(V_{ds}{I}_{ds}+V_{qs}{I}_{qs}\right)$$

(11)

$$Q_s=\left(\frac{3}{2}\right)\left(V_{qs}{I}_{ds}-V_{ds}{I}_{qs}\right)$$

(12)

The following formula is used to determine the active and reactive rotors’ powers:

$$P_r=\left(\frac{3}{2}\right)\left(V_{dr}{I}_{dr}+V_{qr}{I}_{qr}\right)$$

(13)

$$Q_r=\left(\frac{3}{2}\right)\left(V_{qr}{I}_{dr}-V_{dr}{I}_{qr}\right)$$

(14)

It is also possible to rewrite the system equations to account for rotating frames [56]:

$$P_T=P_s+P_r=\left(\frac{3}{2}\right)\left(\dot{V_{qr}}{\dot{I}}_{qr}+\dot{V_{dr}}{\dot{I}}_{dr}+V_{ds}{I}_{ds}+V_{qs}{I}_{qs}\right)$$

(15)

$$Q_T=Q_s+Q_r=\left(\frac{3}{2}\right)\left(\dot{V_{qr}}{\dot{I}}_{qr}-\dot{V_{dr}}{\dot{I}}_{dr}+V_{ds}{I}_{ds}-V_{qs}{I}_{qs}\right)$$

(16)

The torque and the stator side reactive power, which are the main objectives of the rotor side converter control system, have the following form [60]. $I_{qs}$ and $I_{qr}$ are the $q$ component of the stator side and rotor side current, $I_{ds}$ and $I_{dr}$ are the $d$ component of the stator side and rotor side current, $V_{qs}$ and $V_{ds}$ are the $q$ and $d$ components of the stator side voltage, where p is the number of pole sets of the generator. The stator side and rotor side flux linkages and the electromagnetic torque using the d-q elements in the frame of synchronous reference are [61]:

$${\mathsf{\Psi }}_s=L_s{I}_s+L_m{I}_r$$

(17)

$${\mathsf{\Psi }}_r=L_m{I}_s+L_r{I}_r$$

(18)

$$T_m=\frac{3}{2}p\frac{L_m}{L_s}\left({\mathsf{\Psi }}_{qs}{I}_{dr}-{\mathsf{\Psi }}_{ds}{I}_{qr}\right)$$

(19)

3.2. DFIG’s Rotor Side Control

The DFIG’s RSC electrical circuit is accountable for freely controlling the active and reactive powers to maximise the available power. Considering the regular electrical grid, the stator flux φ_s is constant. Furthermore, the stator resistance value is minimal for the moderate and highly rated power DFIGs; consequently, it can be ignored [62,63]. Given the above values, Equations (2) and (3) for the stator voltages and fluxes are much easier to understand [64]:

$$\begin{gathered} V_{ds}=0 \\ {V}_{qs}=V_s={\omega }_s{\phi }_{ds} \end{gathered}$$

(20)

$${\phi }_{ds}={\phi }_{ds}=L_s{i}_{ds}+L_m{i}_{dr}$$

(21)

$${\phi }_{ds}=0=L_r{i}_{qs}+L_m{i}_{dr}$$

(22)

The stator, rotor, and magnetising inductances are designated as L_s, L_r, and L_m, respectively. The active and reactive powers are given by [64]:

$$P_s=\frac{3}{2}\left(V_{ds}{I}_{ds}+V_{qs}{I}_{qs}\right)=-\frac{3}{2}\frac{L_m}{L_s}\left(V_s{I}_{qr}\right)$$

(23)

$$Q_s=\frac{3}{2}\left(V_{qs}{I}_{ds}+V_{ds}{I}_{qs}\right)=\frac{3}{2}\left(\frac{V_s^2}{{\omega }_s{L}_s}-\frac{L_m}{L_s}{V}_s{i}_{dr}\right)$$

(24)

Equations (23) and (24) show that the stator side active and reactive powers are self-governing from each other. Additionally, the elements of stator side power are in linear proportion with the direct and quadrative rotor currents. Power systems typically employ PI controller regulation for the d-axis and q-axis factors of the rotor current and control. The reference current serves as the input for the PI current controller, which measures the reference voltage and controls the current to a constant value to maintain a constant stator flux. The transfer function for the control system is given by:

$$\dot{G}\left(p\right)=\frac{I_{rp}^{*}\left(p\right)}{V_{rq}^{*}\left(p\right)}=\frac{I_{rd}^{*}}{V\left(p\right)}=\frac{1}{R_r+L_r\sigma p}$$

(25)

The closed-loop transfer function is provided by:

$$\dot{H}\left(p\right)=\frac{I_{rq}\left(p\right)}{I_{rq}^{*}\left(p\right)}=\frac{I_{rd}\left(p\right)}{I_{rd}^{*}\left(p\right)}=\frac{\left(K_p^{″}p+K_i^{\prime }\right)\left(L_r\sigma \right)}{S^{\prime }\left(p\right)}$$

(26)

Here, S′(p) is the characteristic polynomial given by:

$$\dot{S}\left(p\right)=p^2+\left(\frac{R_r+K_p^{″}}{L_r\sigma }\right)p+\frac{K_i^{″}}{L_r\sigma }$$

(27)

The PI controller’s two gains for the rotor dynamics imply that:

$$K_i^{″}=2L_r\sigma {\mu }^2$$

(28)

$$K_p^{″}=2L_r\sigma \mu -R_r$$

(29)

The authors considered the PI controller’s upper and lower saturation limits for RSC simulation model construction, $-\frac{V_{bus}}{\sqrt{3}}$ with a gain value of one and a sampling time of $\frac{1}{f_{sw}}$.

3.3. DFIG’s Grid Side Control

The GSC system can be mathematically represented in the MATLAB simulation model. The model uses two PI controllers for each direct and quadrature grid current axis. The d-axis is associated with the grid side vector voltage to implement the VOC scheme. As a result, this causes the d-axis grid voltage to be the same as its magnitude and the q-axis voltage to be zero. Hence, the grid power expression from Equations (23) and (24) is as follows:

$$P_s=\frac{3}{2}{V}_{ds}{I}_{ds}$$

(30)

$$Q_s=-\frac{3}{2}{V}_{ds}{I}_{ds}$$

(31)

$$G\left(p\right)=\frac{P_s^{*}\left(p\right)}{I_{rq}^{*}\left(p\right)}=\frac{Q_s^{*}\left(p\right)}{I_{rd}^{*}\left(p\right)}=\frac{{MV}_s}{L_s{R}_r+L_s{R}_r\sigma p}$$

(32)

$$H\left(p\right)=\frac{P_s\left(p\right)}{I_{rq}^{*}\left(p\right)}=\frac{Q_s\left(p\right)}{Q_s^{*}\left(p\right)}=\frac{\raisebox{1ex}{$\left(K_{p}p+K_i\right)M{V}_s$}\!\left/ \!\raisebox{-1ex}{$L_s{L}_r\sigma $}\right.}{S\left(p\right)}$$

(33)

The PI controller’s two gains for the stator dynamics imply that:

$$K_i^{\prime }=2{\rho }^2\frac{L_s{L}_r\sigma }{M{V}_s}$$

(34)

$$K_p=\frac{L_s{L}_r\sigma }{M{V}_s}\left(2\rho -\frac{R_r}{L_r\sigma }\right)$$

(35)

For the GSC simulation model’s construction, the authors considered the PI controller’s upper and lower saturation limits $P_s{s}_{\max }$, $-P_s{s}_{\max }$ with a gain value of one and a sampling time of $\frac{1}{f_{sw}}$.

3.4. PI Controllers Tuning Problem

In the PI-controlled framework, empirical methods and trial-error-based procedures obtain the appropriate K_p and K_i gains values. These non-systematic and complex activities become more challenging and time-consuming, particularly for sophisticated and large-scale systems, such as the DFIG-based WECS under study. Hence, a promising method is to formulate the selection of the K_p and K_i gains as an optimisation issue. With the help of sophisticated metaheuristics, a control issue of this nature, which can be nonlinear, non-smooth, or even non-convex, can be successfully resolved [64].

3.5. Artificial Neural Network Modelling

The initial stage of model forecast control involves locating the neural network’s plant modelling (system credentials). To predict how a nonlinear plant will operate in the future, the Neural Network Predictive Controller models a neural network. The model then defines the control input required to maximise plant performance from a futuristic time perspective. The control signal that lowers the following performance measures over the distinct possibility is found using a mathematical optimisation technique that uses projections. Figure 3 depicts the neural-predictive controller’s block diagram.

$$j={{\displaystyle \sum }}_{j=n_1}^{n_2}{\left(y_r\left(t+j\right)-y_m{\left(t+j\right)}^2-y_m\left(t+j\right)\right)}^2$$

(36)

$$j={\sum }_{j=1}^{N_u}{\left(u^{\prime }\left(t+j-1\right)-u^{\prime }\left(t+j-2\right)\right)}^2$$

(37)

$$j={\sum }_{j=n_1}^{n_2}\left(y_r\left(t+j\right)-y_m{\left(t+j\right)}^2+p\sum _{j=1}^{n_g}{\left(u^{\prime }\left(t+j-1\right)-u^{\prime }\left(t+j-2\right)\right)}^2\right)$$

(38)

where the horizons for evaluating the tracing errors and control augmentations are determined using n₁, n₂, and N_u. The u’ variable is the uncertain controlled signal, y_r is the anticipated reaction, and y_m is the network’s model reaction. The p-value defines the impact of the summation of squares of control augmentations on the execution guide. Likewise, the generator electromagnetic torque developed in Equation (10), can be written as:

$$T_{em}=p\left({\mathsf{\Psi }}_{ds}{I}_{qs}-{\mathsf{\Psi }}_{qs}{I}_{ds}\right)$$

(39)

In this example, we use a backpropagation algorithm to showcase the feedforward ANN. Figure 4 shows the BP ANN’s basic working schematic diagram [65]. The BP ANN configuration comprises input, hidden, and output layers. Artificial neurons of the hidden and output layers administer input. The concealed layer might have any number of numbers depending on the circumstance and source of the issue.

Neurons in nonlinear controls use the weights and biases, which are parameters associated with each artificial neuron, to process input. With the ith neuron in the hidden layer serving as the reference point, the weight is denoted as w_ij while the threshold is signified as θ_i. Currently, j is the subscript of input (j = 1, 2, …, m) while i is the neuron subscript (i = 1, 2, …, q). As a result, the numerical expression for the neuron equations for nonlinear properties is [66]:

$${net}_i={\sum }_{j=1}^m{w}_{ij}{x}_j+{\theta }_i$$

(40)

The internal component of the expression, in this case, is net_i and the nonlinear characteristics of the neurons as shown in the following equation:

$$y_i=\phi \left({net}_i\right)=\phi \left({\sum }_{j=1}^m{w}_{ij}{x}_j+{\theta }_i\right)$$

(41)

where y_i is the output definition, and φ is an excitation function that considers the neurons’ nonlinear behaviour. The commonly used functions are an S-shaped tangent function (tansig), an S-shaped logarithmic function (logsig) and a purely linear function (purelin). The output layer of neurons executes related controls, and in this example, the kth output o_k is as follows [66]:

$$o_k=\phi \left({net}_k\right)=\phi \left[{\sum }_{i=1}^q{w}_{ki}\phi \left({\sum }_{j=1}^m{w}_{ij}{x}_j+{\theta }_i\right)+a_k\right]$$

(42)

The weight and bias are represented as W_ki and a_k of neuron k in the output layer, separately, while the excitation function is φ. There is no established process for choosing the neuron’s weights. The study emphasises several selection methods, including Xavier initialisation, random weight, and zero weight selection. The weights were changed in this investigation using Xavier initialisation, which initialises them arbitrarily.

4. Methodology

Figure 5 [40] depicts a WECS with a grid-tied DFIG foundation. The aimed ANN control system and the conventional PI control scheme are both intended for simulation tasks in the authors’ research of a 1.0 Mega Watt DFIG-based WECS model. With data collected under various operational and environmental conditions, the authors provided an efficient analysis process of the proposed method and the conventional approach. The system parameters under consideration are provided in

Table 3. DFIG-integrated WECS parameters.

DFIG’s power rating	1.0 MW
System voltage	400 V
System frequency	50 Hz
Magnetic pole sets 2	3
Stator side resistance, Rs	7.06 × 10−3
Stator side inductance, Ls	0.171 mH
Rotor side resistance, Rr	5.0 × 10−3
Rotor side inductance, Lr	0.156 mH
Mutual inductance, Lm	2.9 mH
DC bus link voltage	1000 V
DC bus link capacitance	10 µF
Filter inductance, Lf	300 mH

. The MATLAB R2022b toolbox simulates the implemented model of a grid tied DFIG with a PI and Neural Network Predictive Controller.

The authors used a neural network model of a nonlinear plant using a machine learning neural network predictive controller to forecast the plant’s future behaviour. This controller is a supervisory model. The controller uses the randomly selected data and trains them using the Levenberg–Marquardt algorithm. While training the data, it generates the random control signals for the system and trains them upon the deviation from the reference and output of the system where it has been placed. The controller then decides which control input will maximise plant performance over a designated future time horizon. The controller then uses the model to anticipate future performance. The authors provide instructions on how to identify a system in the section on the optimisation procedure. A discussion of the created predictive controller model block’s application follows.

4.1. System Identification

For the model’s predictive control, the authors taught a neural network to simulate the plant’s forward dynamics. The prediction error between the plant and neural network outputs is used to train the neural network. Figure 6 illustrates the procedure of system identification. The neural network plant model forecasts future values of the plant output by using historical inputs and historical plant outputs. Figure 7 shows the graphical composition of the neural network plant model. This network may be taught offline and in batch mode utilising information from the plant’s operation. The authors trained the network using any training techniques covered in Multilayer Shallow Neural Networks and Backpropagation Training.

The multiple layer propagation (MLP) kind of NN method [67] highly influences an algorithmic association. Additionally, the scholars reviewed various NN formats in [67]. The first proposal was formed on an early NN arrangement of the anticipated input y_p(t) and target U(t) level neurons read out by the numerous individual indicators, which is an unseen level (b) with few neurons and suitable transfer functions (TFs). Smaller arbitrary weights are designated so that the neuron outputs remain un-saturated. The second proposal on the NN arrangement is to use one input design, where the output is intended (predefined as an onward pass) in association with the output design.

The calculated fault sum-squared-error (SSE) or mean-squared-error (MSE) is labelled in advance; the weights are changed in the reverse path using the backpropagation procedure until the fault inclusive of the preferred output design is minor and adequate [67]. In an inadequate fault convergence, the hidden or unseen layers’ neuron numbers need to be improved and subsequently added to an unseen layer(s). The whole SSE of the P arrays pair, as detailed in [67]:

$$SSE=E={\sum }_{p=1}^P{E}_p={\sum }_{p=1}^P{\sum }_{j=1}^Q{\left(d_j^p-y_j^p\right)}^2$$

(43)

As a result of this arrangement, the neuron’s weights improved to curtail the importance of the impartial function SSE with the grade succession method, as stated earlier. The weight amend equation is specified as [67]:

$$W_{ij}\left(k+1\right)=W_{ij}\left(k\right)-\eta \left(\frac{\delta E_p}{\delta W_{ij}\left(k\right)}\right)$$

(44)

The mean square error (MSE = SSE/Q) as the objective function is engaged, where Q is the dimension of the output vector. A thrusting term $\mu \left[W_{ij}\left(k\right)-W_{ij}\left(k-1\right)\right]$ is attached to Equation (44) and considered u < 1.0 as a minor assessment to ensure the SSE meets a global minimum.

4.2. Proposed NNPC-Based DPC Control Design

The authors proposed a MATLAB simulation model to manage active and reactive power and keep the constant DC linkage voltage of the DFIG-integrated WECS under the symmetrical fault condition at the load side. The rotor and grid side controls are created in this part by utilising NNPC methodology. The expression for the power equations is:

$$P_T=P_s+P_r$$

(45)

$$Q_T=Q_s+Q_r$$

(46)

P_s is the active power injected into the grid via the stator side of the DFIG, and P_r is the active power injected via the rotor side of the DFIG. P_T is the total DFIG-based WECS’s active power supplied to the grid. Similarly, Q_T represents the real reactive power of the DFIG-based WECS.

The DFIG’s active and reactive power regulation is accomplished by contemplating the stator flux association on the d-axis. As a result, the quadrature element of the DFIG stator side flux is zero. Therefore, φ_ds = φ_s and φ_qs = 0.

The electromagnetic torque of the DFIG-based WECS is, therefore, expressed as follows:

$$T_{em}=-p\frac{L_m}{L_s}\left({\mathsf{\Psi }}_{ds}{I}_{qr}\right)$$

(47)

Likewise, the DFIG’s stator side active and reactive power can be altered while disregarding the DFIG stator side resistance. Therefore, v_ds and v_qs = v_s.

$$P_s=-v_s\frac{L_m}{L_s}{i}_{qr}$$

(48)

$$Q_s=v_s\frac{{\mathsf{\Psi }}_s}{L_s}{i}_{dr}-v_s\frac{L_m}{L_s}{i}_{dr}$$

(49)

Similarly, the DFIG’s rotor side voltages can be modified, rendering the rotor side currents:

$$v_{dr}=R_r{i}_{dr}+\left(L_r-\frac{L_m^2}{L_s}\right)\frac{{di}_{dr}}{dt}-s·w_s\left(L_r-\frac{L_m^2}{L_s}\right)i_{qr}$$

(50)

$$v_{qr}=R_r{i}_{qr}+\left(L_r-\frac{L_m^2}{L_s}\right)\frac{{di}_{qr}}{dt}+s·w_s\left(L_r-\frac{L_m^2}{L_s}\right)i_{dr}+s·w_s\frac{L_m{v}_s}{w_s{L}_s}$$

(51)

With this $s=\frac{\left(w_s-w_r\right)}{w_s}$ and we may now alter Equations (50) and (51) by ignoring the voltage drops for the slip values, which are comparatively relatively small and can be modified as follows:

$$v_{dr}\approx 0$$

(52)

$$v_{qr}\approx s\frac{L_m{v}_s}{L_s}$$

(53)

Equations (52) and (53), respectively, can be substituted into Equations (13) and (14) to rewrite the active and reactive power of the DFIG rotor. This suggests:

$$P_r=s·\frac{L_m{v}_s}{L_s}·i_{qr}$$

(54)

$$Q_r=s·\frac{L_m{v}_s}{L_s}·i_{dr}$$

(55)

To simplify Equations (45) and (46), which represent the total grid side active and reactive powers, Equations (48), (49), (54), and (55) may be substituted instead.

$$P_T=\left(s-1\right)·v_s·\frac{L_m}{L_s}·i_{qr}$$

(56)

$$Q_T=\frac{v_s^2}{w_s{L}_s}+\left(s-1\right)·v_s·\frac{L_m}{L_s}·i_{dr}$$

(57)

Equations (55) and (56) describe the total power that the rotor side converter controller must handle to achieve superior performance compared to a standard converter. To construct and apply an ANN-based optimum training control, as expressed in Equations (56) and (57), a discrete quantity can be represented using:

$$P_T\left(k+1\right)=\left(s-1\right)·v_s\left(k+1\right)·\frac{L_m}{L_s}·i_{qr}\left(k+1\right)$$

(58)

$$Q_T\left(k+1\right)=\frac{v_s^2{\left(k+1\right)}^2}{w_s{L}_s}+\left(s-1\right)·v_s\left(k+1\right)·\frac{L_m}{L_s}·i_{dr}\left(k+1\right)$$

(59)

The predicted value for the following sample is now (k + 1) and must be calculated arithmetically. However, the direct linking between the stator side windings and the grid ensures that the DFIG’s stator voltage stays steady and equal to the grid side voltage. Hence:

$$v_s\left(k+1\right)=v_s\left(k\right)$$

(60)

The d-q components of the rotor side current i_dr(k + 1) and i_qr(k + 1) are represented using discrete quantities. Equations (50) and (51), then, can be written as:

$$i_{dr}\left(k+1\right)=i_{dr}\left(k\right)+T_{s}M\left[v_{dr}\left(k\right)-i_{dr}\left(k\right)R_r\right]+T_{s}s{w}_s{i}_{qr}\left(k\right)$$

(61)

$$i_{qr}\left(k+1\right)=i_{qr}\left(k\right)+T_{s}M\left[v_{qr}\left(k\right)-i_{dr}\left(k\right)R_r\right]-T_{s}s{w}_s{i}_{qr}\left(k\right)-T_{s}Ms\frac{L_m{v}_s\left(k\right)}{L_s}$$

(62)

Here, T_s is the sampling time and $M=\left(L_r-\frac{L_m^2}{L_s}\right)$ in the proposed RSC side controller using NNPC. Now, the RSC side output voltage of the power inverter is seen as a restriction. Equations (64) and (65) represent the inequality resulting from the fact that the inverter output amplitude is dependent on the magnitude of the input DC voltage.

$$-v_{dc}<v\left(k\right)<v_{dc}$$

(63)

Considering the initialisation of all the variables as zero and subjected to Equations (59)–(63), the optimisation problem can be formulated as Equations (64) and (65).

$$Minimise obj={\sum }_{k=0}^m\left(P_T^{*}\left[k+1\right]-P_T{\left[k+1\right]}^2\right)$$

(64)

$$Minimise obj={\sum }_{k=0}^m\left(Q_T^{*}\left[k+1\right]-Q_T{\left[k+1\right]}^2\right)$$

(65)

The above optimisation issue is resolved using a precise optimisation solver and utilised to recognise the optimal locations of v_dr, v_qr, i_dr and i_qr for the anticipated active and reactive power regulation.

Table 4. DFIG grid side and the rotor side neural network control training data.

S.no	Grid Side Dataset		Rotor Side Dataset
	Input1 (Error from the Reference and the Output of the System)	Controller Output1	Input2 (Error from the Reference and the Output of the System)	Controller Output2
1	0	4.81242 × 10−5	0	−0.000157489
2	−3.09322 × 10−31	4.81242 × 10−5	1.00109 × 10−30	−0.000157489
3	−0.000405531	−0.000139566	6.31395 × 10−5	−4.5304 × 10−5
4	−0.002343437	−0.001060369	3.12447 × 10−5	0.000188963
5	−0.006585896	−0.003418563	−0.000163214	0.000509639
6	−0.014727456	−0.009603213	−0.000576467	0.000708515
7	−0.027209002	−0.02348748	−0.000977557	0.000373323
8	−0.037539492	−0.038113975	−0.000928672	2.20362 × 10−5
9	−0.045514179	−0.05039214	−0.000633667	−9.50781 × 10−5
10	−0.049421172	−0.056452314	−0.000450451	−0.000137974
11	−0.049421172	−0.056452314	−0.000450451	−0.000137974
12	−0.053237069	−0.062278347	−0.000297303	−0.000233139
13	−0.056504717	−0.067138904	−0.000390717	−0.000615214
14	−0.058490317	−0.070037076	−0.00074835	−0.001241152
15	−0.059075664	−0.070909618	−0.00138214	−0.002107146
16	−0.058362313	−0.069912755	−0.002266591	−0.003189317
17	−0.057446144	−0.068582557	−0.002866534	−0.00389058
18	−0.057446144	−0.068582557	−0.002866534	−0.00389058
19	−0.033039115	−0.031203846	−0.003752168	−0.00309742
20	−0.021422702	−0.016277536	−0.004685421	−0.003671495
21	−0.01499355	−0.009832681	−0.005402891	−0.00441528
22	−0.008969182	−0.005118821	−0.006173201	−0.005399405
23	−0.004556981	−0.002412339	−0.006724242	−0.006220265
24	−0.002430339	−0.00127843	−0.006868558	−0.006517577
25	−0.001331156	−0.000703263	−0.006711327	−0.006436225
26	−0.00076513	−0.00037922	−0.006269037	−0.006025372
27	−0.000494377	−0.000186618	−0.005563169	−0.00533149
28	−0.000387145	−7.46769 × 10−5	−0.00463325	−0.004415341
29	−0.000360145	−2.0409 × 10−5	−0.00353096	−0.003346833
30	−0.000355	−1.1087 × 10−5	−0.002312209	−0.002196211
31	−0.000329316	−3.66353 × 10−5	−0.001031187	−0.001027062
32	−0.000253815	−8.69588 × 10−5	0.000263067	0.000107694
33	−0.000111398	−0.000151652	0.001527966	0.001167107
34	0.000103689	−0.00022057	0.002727196	0.002121635
35	0.000387089	−0.000284445	0.003829723	0.002951523
36	0.000725855	−0.000335238	0.004808497	0.00364481
…	…………	……….	…………………	………………….
…	…………	……….	…………………	………………….
999	−4.35895 × 10−5	1.53771 × 10−5	0.000167348	−5.45681 × 10−6
1000	5.97742 × 10−5	5.92646 × 10−5	0.000194555	3.44725 × 10−6

provides the random data values in p.u.

Using the dynamic equation between the DC input power to the GSC and the DC output power added to the power grid, or vice versa from the rotor side, the ANN control model strives to conserve the DC link voltage at the anticipated set value. Now, the power assessment equation of the DC bus capacitance is:

$$\left(C_{dc}\frac{{dv}_{dc}}{dt}\right)v_{dc}=\left(v_{gd}{i}_{gd}+v_{gq}{i}_{gq}\right)$$

(66)

where V_dc is the DC link voltage, C_dc is the DC link capacitor, V_gd and V_gq are the grid side d-q axis voltages, i_gd and i_gq are the grid side current dynamic equations employing an inductance filter in the d-q axis, and these equations are discretised and written as:

$$v_{dc}\left(k+1\right)=v_{dc}\left(k\right)+\frac{T_s\left[v_{gd}\left(k\right)i_{gd}\left(k\right)-v_{gq}\left(k\right)i_{gq}\left(k\right)\right]}{C_{dc}{v}_{dc}\left(k\right)}$$

(67)

$$i_{gd}\left(k+1\right)=i_{gd}\left(k\right)+T_s\left[\frac{r_g{i}_{gd}\left(k\right)}{L_f}+w_s{i}_{gq}\left(k\right)\right]+T_s\left[\frac{v_{gd}\left(k\right)}{L_f}-\frac{u_{gd}\left(k\right)}{L_f}\right]$$

(68)

The GSC filter’s inductance is L_f, its resistance is r_g, and its output voltages are u_gd and u_gq before the filter. The optimisation problem formulation for the DC bus voltage control is answered by considering the initialisation of all the variables as zero and subjected to the above Equations (67) and (68), which can be represented as:

$$Minimise obj={\sum }_{k=0}^m\left(V_{dc}^{*}\left[k+1\right]-V_{dc}{\left[k+1\right]}^2\right)$$

(69)

With Equations (64) and (65), which define the objective function, and initial conditions of zero, the PSO optimisation method is used to discover the optimum values, considering restrictions such as the lowest and maximum values of the variables and active and reactive powers. The ANN model trains the block using these ideal values to operate the DFIG-based WECS.

The optimum values of i_gd and i_gq and u_gd and u_gq have been discovered to train the ANN block for the grid side control. Similarly, the objective function determined in Equation (69) is answered using a similar process as indicated before for the optimal values.

4.3. Datasets

The authors used the two random data base sets, specifically the DFIG rotor side and the grid side data of 1000, for the proposed NN model to see, learn, and validate the data to optimise the DFIG-integrated grid system’s stability under the three-phase fault occurrence. A detailed description of the employed dataset’s values in p.u. is given in Table 4.

As a result, the NNPC controller is trained using random sampling data to discover these ideal control actions. The training dataset size must be larger than the validation and testing dataset size. Since the proposed model has few hyperparameters, the authors used a reduced testing size and the validation set. To offer a consistent training and testing procedure for each dataset, a technique known as stratified-based random sampling was applied. A stable system was something the creators were after.

The proposed NNPC controller’s design aims to mimic optimum control behaviour in real-time implementations. In this article, the RSC and GSC are controlled with a BP neural network.

Table 5. NNPC parameters.

Parameter	Values
Cost horizon (N2)	2
Cost horizon (Nu)	2
Control weight factor	0.1
Search parameter	0.1
Iterations per sample	5
Hidden layer size	5
Sample interval	1
No. of delayed plant inputs	1
No. of delayed plant outputs	1
Maximum plant input	1
Minimum plant input	0
Training epochs	5

indicates the BP network’s specifications. Hence, in a 60/20/20 split, the data base sets in Table 4 and Table 5 are utilised for training, testing, and validation, respectively. It is then readily available to be used in the GSC and RSC control operating system to accomplish the intended DFIG-based WECS control goals under symmetrical fault situations.

Data Validation Assessment

The authors of this study gained knowledge of how to teach neural networks to map predictors to continuous responses. In this investigation, the Levenberg–Marquardt method was employed. The desired number of characteristics may be selected with the aid of this algorithm. Additionally, this method has improved accuracy and effort reduction performance. Performance is monitored as the amount of the selected property changes, and the dataset is utilised to establish the appropriate number of features. Memorisation may come from the excessive selection of data used in schooling. The authors suggested that no more than 80% of the available samples be used throughout the training procedure to prevent excessive data selection. Simple data requirements for the predictors include a double array of 94 observations with a single feature. Similarly, to the data specifications reply, the simple fit objective is a double array of 94 observations with a single element. The training dataset was used with a layer size of 10.

The authors used only 200 samples out of every 1000 for actual training. Figure 8 and Figure 9 represent the training state fitting plot and the best data validation performance achieved. Similarly, the achieved mean square error (MSE) using the 20 bins presented in Figure 10 is reasonably good, with a smaller MSE result. A smaller MSE indicates a minor loss, which shows a better model. The achieved regression error distributions, presented in Figure 11, are reasonably good and distributed relatively close to the perfect prediction, yielding a decent R² score. The data presented in

Table 6. Training progress.

Unit	Initial Value	Stopped Value	Target Value
Epoch	0	191	1000
Elapsed time	-	00:00:00	-
Performance	76	5.8 × 10−5	0
Gradient	161	1.43 × 10−5	1.0 × 10−7
Mu	0.001	1.0 × 10−7	1.0 × 1010
Validation check	0	6	6

and

Table 7. Training results.

Unit	Initial Value	Stopped Value	Target Value
Training	66	5.8030 × 10−5	1.0000
Validation	14	2.9528 × 10−5	1.0000
Test	14	4.9291 × 10−5	1.0000

are the outcomes of the simulation processes training progress and results status.

5. Results

The proposed ANN control methodology and the traditional PI control method are used for simulation tasks. With the aid of the data collected under various operational and environmental settings, the authors examine the efficacy of the recommended method in this section. Table 1 lists the specifications of the system under review. A grid-tied DFIG with a PI and Neural Network Predictive Controller is constructed as a model in the MATLAB R2022b toolbox.

5.1. Wind Speed Variations

To assess the simulation findings, the authors included the environmental change in wind speed, with changing wind speed ranging from 4 m/s to 20 m/s as the wind turbine input. Both controllers were tested in the 4 m per second to 20 m per second wind speed range, as shown in Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, Figure 30, Figure 31, Figure 32, Figure 33, Figure 34, Figure 35, Figure 36, Figure 37, Figure 38, Figure 39, Figure 40, Figure 41, Figure 42, Figure 43, Figure 44, Figure 45, Figure 46, Figure 47 and Figure 48, even though both controllers offered good performance. However, the NNPC system responded considerably more quickly and had a significantly smaller transitory region due to the decreased processing cost of the finite control set. This trait helps to manage fluctuating winds more effectively by regulating the power output to reduce the effects of peak demand.

The NNPC system had a quicker dynamic reaction regarding system dependability than the PI control system when the authors considered the DFIG’s active and reactive power, mechanical and electrical torque T_g, DC bus voltage, and grid side current. Due to quicker tracking and corrective measures, this reaction suggests that NNPC can sustain improved grid-tied DFIG stability under fault conditions. Section 5.2, Section 5.3, Section 5.4, Section 5.5 and Section 5.6 analyse the simulation findings in great detail.

5.2. DFIG Active and Reactive Powers

5.2.1. DFIG Active Power

For the active power generation using a WECS and its injection into the grid, the reactions of the NNPC and PI control schemes are compared in this section. As indicated in Figure 12, Figure 13, Figure 14, Figure 15 and Figure 16, the comparisons are made at various wind speeds ranging from 4 m/s to 16 m/s.

The PI control scheme and NNPC scheme are utilised to examine the WECS’s behaviour during the 50 s of the simulation period under a change in wind speed in the DFIG active power. The active power waveforms exhibit different dynamic and transient behaviours when created using the suggested NNPC and the conventional PI techniques. The authors conducted simulation work at various wind speeds while setting up a three-phase fault with a 1-s duration (from 10 to 11 s) to the load side in the proposed model of the DFIG. The results are analysed in the following ways:

As seen in Figure 12, the NNPC system oscillates less when the wind speed is 4 m/s. Additionally, it cleverly dampens the amplitude modulations over the fault occurrence time of 1 s (from +0.587395 p.u. to −0.38125 p.u.). The DFIG’s active power was enhanced by the NNPC system from −2.72778 p.u. to +0. 9953 p.u., quickly from 11.4393 s to 11.5168 s, then stabilised at a value close to 1.0 p.u. at 14.02 s. The PI control system, on the other hand, exhibits higher oscillations on the amplitude modulations throughout a 1-s failure. Second, the PI control displayed spike amplitude variations in the DFIG’s active power, ranging from 0.995336 p.u. to a value of −3.08574 p.u. between 11.00 s and 11.0211 s before stabilising at 1.0 p.u., value at 14.2 s.

Figure 12. DFIGs active power analysis, NNPC vs. PI control system at 4 m/s of wind speed.

Figure 12. DFIGs active power analysis, NNPC vs. PI control system at 4 m/s of wind speed.

As seen in Figure 13, the NNPC system oscillates less when the wind speed is 6 m/s. Additionally, it cleverly dampens the amplitude modulations across the fault occurrence time of 1 s (from +0.687793 p.u. to +0.353574 p.u.). The NNPC system from −2.73355 p.u. increased the DFIG’s reactive power to +0.992803 p.u., swiftly from 11.4629 s to 11.629 s, and stabilised at +1.0 p.u. value at 11.71 s. The PI control system, on the other hand, exhibits higher oscillations on the amplitude modulations throughout a 1-s failure. The PI control, on the other hand, displayed spiky amplitude variations in the DFIG’s active power, ranging from 0.992803 p.u. to a value of −3.10907 p.u. between 11 and 11.0217 s before stabilising at +1.0 p.u. value at 12.52 s.

Figure 13. DFIGs active power analysis, NNPC vs. PI control system at 6 m/s of wind speed.

Figure 13. DFIGs active power analysis, NNPC vs. PI control system at 6 m/s of wind speed.

At 8 m/s of wind speed, as shown in Figure 14, the NNPC system has fewer oscillations. Further, it smartly dampens the amplitude modulations (from +0.583642 p.u. to −0.0402709 p.u.) over the fault occurrence duration of 1 s. The NNPC system improved the DFIG’s reactive power from −2.71942 p.u. to +0.994375 p.u., quickly from 11.4618 s to 12.129 s, and stabilising close to +0.694875 p.u. value at 12.51 s. On the other hand, the PI control system has more oscillations in the amplitude modulations over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s active power from 0.994375 p.u. to a value of −3.1013 p.u. from 11 s to 11.0214 s and stabilised close to +0.69575 p.u. value at 12.52 s.

Figure 14. DFIGs active power analysis, NNPC vs. PI control system at 8 m/s of wind speed.

Figure 14. DFIGs active power analysis, NNPC vs. PI control system at 8 m/s of wind speed.

At 10 m/s of wind speed, as shown in Figure 15, the NNPC system has fewer oscillations. Further, it smartly dampens the amplitude modulations (from +0.364014 p.u. to −0.188284 p.u.) over the fault occurrence duration of 1 s. The NNPC system improved the DFIG’s reactive power from −2.75969 p.u. to +0.336435 p.u., quickly from 11.4393 s to 11.6147 s, and stabilising at 0.42056 p.u. value at 11.72 s. On the other hand, the PI control system has more oscillations in the amplitude modulations over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s active power from +0.926663 p.u. to a value of −3.06331 p.u. from 11 s to 11.0209 s and stabilised at 0.42056 p.u. value at 11.52 s.

Figure 15. DFIGs active power analysis, NNPC vs. PI control system at 10 m/s of wind speed.

Figure 15. DFIGs active power analysis, NNPC vs. PI control system at 10 m/s of wind speed.

At 12 m/s of wind speed, as shown in Figure 16, the NNPC system has amplitude modulations (from +0.48108 p.u. to +0.352744 p.u.) over the fault occurrence duration of 1 s. The NNPC system improved in gaining the DFIG’s active power to a value from −2.67108 p.u. to +0.3546 p.u., quickly from 11.4617 s to 11.8268 s, and stabilised at 0.44809 p.u. value. On the other hand, the PI control system has more amplitude oscillations from +0.0958262 p.u. to +0.999815 p.u. over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s active power to a value from 0.999815 p.u. to −3.0868 p.u. from 11 s to 11.0212 s and stabilised at 0.43251 p.u. value at 11.5246 s.

Figure 16. DFIGs active power analysis, NNPC vs. PI control system at 12 m/s of wind speed.

Figure 16. DFIGs active power analysis, NNPC vs. PI control system at 12 m/s of wind speed.

The suggested ANN control approach achieves better overall results because it settles faster and causes less overshoot during transient operation. In addition, it delivers a superior output since it dampens oscillations faster and has a lower ripple content than the typical PI control method.

5.2.2. DFIG Reactive Power

The reactive power generation using a WECS and its injection into the grid at various wind speeds, 4 m per second to 20 m per second, is shown in Figure 17, Figure 18, Figure 19, Figure 20, Figure 21 and Figure 22. The PI control and NNPC schemes are utilised to analyse the WECS’s behaviour over 50 s of the simulation period under a wind speed change in the DFIG’s reactive power. The proposed NNPC and standard PI methodologies produce different dynamic and transient behaviours of the reactive power waveforms. In the proposed model of the DFIG, the authors established a three-phase fault to the load side with a 1-s duration (from 10 s to 11 s) and carried out the simulation work at various wind speeds. The results are analysed in the following ways:

At 4 m/s of wind speed, as shown in Figure 17, the NNPC system has fewer oscillations. Further, it smartly dampens the amplitude modulations from +0.50081 p.u. to −0.120725 p.u. over the fault occurrence duration of 1 s. The NNPC system increased the DFIG’s reactive power from −3.37536 to +0.825174, swiftly from 11.4447 to 11.5155, then stabilising at close to +0.45890 at 11.62 s. On the other hand, the PI control system has more oscillations in the amplitude modulations over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s reactive power from 1.66219 p.u. to a value of –1.2356 p.u. from 11.0151 s to 11.0211 s and stabilised at +0.45890 p.u. value at 11.72 s.

Figure 17. DFIGs reactive power analysis, NNPC vs. PI control system at 4 m/s of wind speed.

Figure 17. DFIGs reactive power analysis, NNPC vs. PI control system at 4 m/s of wind speed.

At 6 m/s of wind speed, as shown in Figure 18, the NNPC system has fewer oscillations. Further, it smartly dampens the amplitude modulations from +0.500003 p.u. to −0.127539 p.u. over the fault occurrence duration of 1 s. The NNPC system improved the DFIG’s reactive power from −3.04729 p.u. to +0.836017 p.u., quickly from 11.4438 s to 11.5144 s, and stabilising at +0.45890 p.u. value at 11.71 s. The PI control system, in contrast, exhibits higher oscillations on the amplitude modulations throughout a 1-s failure. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s reactive power from 1.65292 p.u. to a value of −1.2356 p.u. from 11.0147 s to 11.0217 s and stabilised at +0.45890 p.u. value at 11.75 s.

Figure 18. DFIGs reactive power analysis, NNPC vs. PI control system at 6 m/s of wind speed.

Figure 18. DFIGs reactive power analysis, NNPC vs. PI control system at 6 m/s of wind speed.

At 8 m/s of wind speed, as shown in Figure 19, the NNPC system has fewer oscillations. Further, it smartly dampens the amplitude modulations (from +0.500309 p.u. to −0.230327 p.u.) over the fault occurrence duration of 1 s. The NNPC system improved the DFIG’s reactive power from −2.72541 p.u. to +0.825114 p.u., quickly from 11.4434 s to 11.4956 s, and stabilising close to +0.50890 p.u. value at 11.62 s. On the other hand, the PI control system has more oscillations in the amplitude modulations over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s reactive power from 1.5926 p.u. to a value of –1.2356 p.u. from 11.0142 s to 11.0221 s and stabilised at +0.50890 p.u. value at 11.65 s.

Figure 19. DFIGs reactive power analysis, NNPC vs. PI control system at 8 m/s of wind speed.

Figure 19. DFIGs reactive power analysis, NNPC vs. PI control system at 8 m/s of wind speed.

At 10 m/s of wind speed, as shown in Figure 20, the NNPC system has fewer oscillations. Further, it smartly dampens the amplitude modulations (from +0.498499 p.u. to −0.433483 p.u.) over the fault occurrence duration of 1 s. The NNPC system improved the DFIG’s reactive power from −2.85846 p.u. to +0.856435 p.u., quickly from 11.4436 s to 11.5147 s, and stabilising at +0.495840 p.u. value at 11.69 s. On the other hand, the PI control system has more oscillations in the amplitude modulations over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s reactive power from 1.63642 p.u. to a value of –1.2356 p.u. from 11.0156 s to 11.0221 s and stabilised at +0.496540 p.u. value at 11.72 s.

Figure 20. DFIGs reactive power analysis, NNPC vs. PI control system at 10 m/s of wind speed.

Figure 20. DFIGs reactive power analysis, NNPC vs. PI control system at 10 m/s of wind speed.

At 12 m/s of wind speed, as shown in Figure 21, the NNPC system has fewer oscillations. Further, it smartly dampens the amplitude modulations (from +0.497576 p.u. to −0.22814 p.u.) over the fault occurrence duration of 1 s. The NNPC system improved the DFIG’s reactive power from −3.24589 p.u. to +0.796511 p.u., quickly from 11.4443 s to 11.4968 s, and stabilising close to +0.50890 p.u. value at 11.62 s. On the other hand, the PI control system has more oscillations in the amplitude modulations over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s reactive power from 1.65575 p.u. to a value of –1.2356 p.u. from 11.015 s to 11.0221 s and stabilised at +0.50890 p.u. value at 11.70 s.

Figure 21. DFIGs reactive power analysis, NNPC vs. PI control system at 12 m/s of wind speed.

Figure 21. DFIGs reactive power analysis, NNPC vs. PI control system at 12 m/s of wind speed.

At 20 m/s of wind speed, as shown in Figure 22, the NNPC system has fewer oscillations. Further, it smartly dampens the amplitude modulations (from +0.499581 p.u. to −0.303208 p.u.) over the fault occurrence duration of 1 s. The NNPC system improved the DFIG’s reactive power from −2.15374 p.u. to +0.960916 p.u., quickly from 11.4424 s to 11.4951 s, and stabilising at +0.495840 p.u. value at 11.69 s. On the other hand, the PI control system has more oscillations in the amplitude modulations over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked amplitude variation in the DFIG’s reactive power from 1.56047 p.u. to a value of –1.2356 p.u. from 11.0141 s to 11.0231 s and stabilised at +0.496540 p.u. value at 11.75 s.

Figure 22. DFIGs reactive power analysis, NNPC vs. PI control system at 20 m/s of wind speed.

Figure 22. DFIGs reactive power analysis, NNPC vs. PI control system at 20 m/s of wind speed.

The improved power quality seen in the waveform is attributed to the NNPC’s strategy. Good power quality behaviour suggests a shorter time required to reach the reference reactive power level during steady-state operation. Additionally, the ripple of the waveform is lessened compared to the typical one. The conventional control strategy has a steady-state error after the settling period and exhibits poor settling time. The slow reaction and transient peak, which are indicators of poor control performance during the WECS’s transient and steady-state operations, are over the upper limit. Therefore, it is evident that the proposed NNPC controller outperformed the PI controller in terms of results.

5.3. DC Bus Voltage Control Waveform

Figure 23, Figure 24, Figure 25, Figure 26, Figure 27 and Figure 28 shows the behaviour of the DC bus link voltage waveform during the transient fault simulation analysis. The proposed concept of the DFIG with the NNPC system involves setting up a three-phase fault to the load side that lasts for one second (10–11 s). The authors compared the proposed NNPC scheme’s performances with the PI control scheme and analysed the visible outcome. The proposed ANN control has a superior output and astonishing transient and dynamic performance to maintain the DC bus link voltage at the proper level. Conventional PI control has a poor quick response due to the high ripple waveform. The time taken to reach the steady state is significant, and a slight steady-state error is present after 11 s. The high DC bus link voltage occurs in the PI control case. Waveform ripples that result from conventional control transfer disturbances to the turbine/generator side, cause stress problems and minute variations in speed from the steady state. Figure 23, Figure 24, Figure 25, Figure 26, Figure 27 and Figure 28 demonstrate how the proposed strategy minimises the ripple to avoid the aforementioned problems.

At 4 m/s of wind speed, as shown in Figure 23, the NNPC system had a DC bus voltage of 1000.64 volts before the fault condition developed. However, during the fault condition, between 10 s and 11 s, the DC bus voltage reached a maximum deviation of 4554.35 volts at 10.1885 s, with fewer ripples and a steady-state condition reached at 11.0132 s. On the other hand, the PI control system has higher DC bus voltage in the range of 9000 volts to 10,000 volts over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked gain in the DC bus voltage to 9940.41 volts from 10.00 s to 11.0205 s, with a delayed response, stabilising at 1000.64 volts at 12.228 s.

Figure 23. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 4 m/s of wind speed.

Figure 23. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 4 m/s of wind speed.

At 6 m/s of wind speed, as shown in Figure 24, the NNPC system had a DC bus voltage of 1001.07 volts before the fault condition developed. However, during the fault condition, between 10 s and 11 s, the DC bus voltage had reached a maximum deviation of 5105.76 volts at 10.1843 s, with fewer ripples down to 850.96 volts, and thereafter, a steady-state condition reached at 11.0051 s. On the other hand, the PI control system had a higher DC bus voltage in the range of 11,000 volts to 11,500 volts over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked gain in the DC bus voltage to 11084.8 volts from 10.00 s to 11.0422 s, with a delayed response, stabilising at 1001.07 volts at 12.51 s.

Figure 24. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 6 m/s of wind speed.

Figure 24. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 6 m/s of wind speed.

At 8 m/s of wind speed, as shown in Figure 25, the NNPC system had a DC bus voltage of 1006.08 volts before the fault condition developed. However, during the fault condition, between 10 s and 11 s, the DC bus voltage reached a maximum deviation of 4647.81 volts at 10.1082 s, with fewer ripples and a steady-state condition reached at 11.0641 s. On the other hand, the PI control system had a higher DC bus voltage above the range of 10,000 volts over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked gain in the DC bus voltage to 10060.5 volts from 10.00 s to 11.0454 s, with a delayed response, stabilising at 1018.57 volts at 12.728 s.

Figure 25. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 8 m/s of wind speed.

Figure 25. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 8 m/s of wind speed.

At 10 m/s of wind speed, as shown in Figure 26, the NNPC system had a DC bus voltage of 1000.5 volts before the fault condition developed. However, during the fault condition, between 10 s and 11 s, the DC bus voltage reached a maximum deviation of 4208.21 volts at 10.1761 s, with fewer ripples down to 950.96 volts, and thereafter, reaching a steady-state condition of 1001.85 DC volts at 11.2535 s. On the other hand, the PI control system has s higher DC bus voltage in the range of 9000 volts to 10,000 volts over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked gain in the DC bus voltage to 9178.28 volts from 10.00 s to 11.0637 s, with a delayed response, stabilising at 1001.85 volts at 12.51 s.

Figure 26. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 10 m/s of wind speed.

Figure 26. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 10 m/s of wind speed.

At 12 m/s of wind speed, as shown in Figure 27, the NNPC system had a DC bus voltage of 1000.12 volts before the fault condition developed. However, during the fault condition, between 10 s and 11 s, the DC bus voltage reached a maximum deviation of 4040.46 volts at 10.1416 s, with fewer ripples and a steady-state condition reached at 11.0641 s. On the other hand, the PI control system had a higher DC bus voltage above the range of 8000 volts over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked gain in the DC bus voltage to 8641.18 volts from 10.00 s to 11.2762 s, with a delayed response, stabilising at 1000.12 volts at 12.68 s.

Figure 27. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 12 m/s of wind speed.

Figure 27. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 12 m/s of wind speed.

At 20 m/s of wind speed, as shown in Figure 28, the NNPC system had a DC bus voltage of 999.885 volts before the fault condition developed. However, during the fault condition, between 10 s and 11 s, the DC bus voltage reached a maximum deviation of 3442.45 volts at 10.1413 s, with fewer ripples down to 959.156 volts, and thereafter, reaching a steady-state condition of 999.885 DC volts at 11.2535 s. On the other hand, the PI control system had a higher DC bus voltage in the range of 8000 volts to 9000 volts over the fault occurrence duration of 1 s. Secondly, the PI control showed a spiked gain in the DC bus voltage to 8995.19 volts from 10.00 s to 11.4594 s, with a delayed response, stabilising at 999.885 volts at 12.805 s.

Figure 28. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 20 m/s of wind speed.

Figure 28. DFIGs DC bus voltage analysis, NNPC vs. PI control system at 20 m/s of wind speed.

5.4. Grid Side Current Waveforms

Figure 29, Figure 30, Figure 31, Figure 32, Figure 33, Figure 34, Figure 35 and Figure 36 show the grid interaction and the stator current behaviours in the waveforms with both control schemes. The stator current is clearly showing satisfactory results with both control schemes. In the proposed model of the DFIG with NNPC, a three-phase fault is established to the load side with a 1-s duration (10 s to 11 s). The waveform is a transient condition at the 11th second due to changes in the I_q grid current and I_d grid current at varying wind speeds at the time of the fault’s occurrence. The ANN performs better during transients in the grid side current than the conventional method; however, the margin of improvement is slightly better.

At 4 m/s of wind speed, as shown in Figure 29 and Figure 30, while simulating the NNPC system, the (d-q) axis current I_d has fewer oscillations, which further dampens down the amplitude modulations from −0.0931398 amps to −0.117086 amps and the I_q from −0.00199687 amps to +0.463976 amps smartly over the fault occurrence duration of 1 s, stabilised at 15.02 s and 12.19 s, respectively. On the other hand, in the PI control system, the (d-q) axis current I_d has more amplitude oscillations from −0.0931398 amps to −0.133235 amps and the I_q from −0.00199687 amps to +0.474912 amps over the fault occurrence duration of 1 s, before settling down at 14.9271 s.

Figure 29. DFIGs grid side d-q axis i_d current analysis, NNPC vs. PI control system at 4 m/s of wind speed.

Figure 29. DFIGs grid side d-q axis i_d current analysis, NNPC vs. PI control system at 4 m/s of wind speed.

Figure 30. DFIGs grid side d-q axis I_q current analysis, NNPC vs. PI control system at 4 m/s of wind speed.

Figure 30. DFIGs grid side d-q axis I_q current analysis, NNPC vs. PI control system at 4 m/s of wind speed.

At 6 m/s of wind speed, as shown in Figure 31 and Figure 32, while simulating the NNPC system, the (d-q) axis current I_d has fewer oscillations, which further dampens down the amplitude modulations from −0.205465 amps to −0.283805 amps (Figure 30) and the I_q from −0.00560673 amps to +0.459598 amps (Figure 32) smartly over the fault occurrence duration of 1 s, stabilised at 15.4245 s and 14.99 s, respectively. On the other hand, in the PI control system, the (d-q) axis current I_d has more amplitude oscillations from −0.205465 amps to −0.147967 amps (Figure 30) and the I_q from −0.00445024 amps to +0.484423 amps (Figure 32) over the fault occurrence duration of 1 s, before settling down at 12.18 s.

Figure 31. DFIGs grid side d-q axis i_d current analysis, NNPC vs. PI control system at 6 m/s of wind speed.

Figure 31. DFIGs grid side d-q axis i_d current analysis, NNPC vs. PI control system at 6 m/s of wind speed.

Figure 32. DFIGs grid side d-q axis I_q current analysis, NNPC vs. PI control system at 6 m/s of wind speed.

Figure 32. DFIGs grid side d-q axis I_q current analysis, NNPC vs. PI control system at 6 m/s of wind speed.

At 8 m/s of wind speed, as shown in Figure 33 and Figure 34, while simulating the NNPC system, the (d-q) axis current I_d has fewer oscillations, which further dampens down the amplitude modulations from −0.1279 amps to −0.128472 amps (Figure 33) and the I_q from −0.002412 amps to +0.449759 amps (Figure 35) smartly over the fault occurrence duration of 1 s, stabilised at 15.02 s and 12.19 s, respectively. On the other hand, in the PI control system, the (d-q) axis current I_d has more amplitude oscillations from −0.1279 amps to −0.124894 amps and the I_q from −0.002412 amps to +0.483977 amps over the fault occurrence duration of 1 s, before settling down at 14.9271 s.

Figure 33. DFIGs grid side d-q axis i_d current analysis, NNPC vs. PI control system at 8 m/s of wind speed.

Figure 33. DFIGs grid side d-q axis i_d current analysis, NNPC vs. PI control system at 8 m/s of wind speed.

Figure 34. DFIGs grid side d-q axis I_q current analysis, NNPC vs. PI control system at 8 m/s of wind speed.

Figure 34. DFIGs grid side d-q axis I_q current analysis, NNPC vs. PI control system at 8 m/s of wind speed.

At 10 m/s of wind speed, as shown in Figure 35 and Figure 36, while simulating the NNPC system, the (d-q) axis current I_d has fewer oscillations, which further dampens down the amplitude modulations from −0.0370604 amps to −0.119728 amps (Figure 34) and the I_q from −0.001238 amps to +0.460542 amps (Figure 36) smartly over the fault occurrence duration of 1 s, stabilised at 15.4245 s and 14.99 s, respectively. On the other hand, in the PI control system, the (d-q) axis current I_d has more amplitude oscillations from −0.0370604 amps to −0.13295 amps (Figure 34) and the I_q from −0.00017633 amps to +0.484423 amps (Figure 36) over the fault occurrence duration of 1 s, before settling down at 12.18 s.

Figure 35. DFIGs grid side d-q axis i_d current analysis, NNPC vs. PI control system at 10 m/s of wind speed.

Figure 35. DFIGs grid side d-q axis i_d current analysis, NNPC vs. PI control system at 10 m/s of wind speed.

Figure 36. DFIGs grid side d-q axis I_q current analysis, NNPC vs. PI control system at 10 m/s of wind speed.

Figure 36. DFIGs grid side d-q axis I_q current analysis, NNPC vs. PI control system at 10 m/s of wind speed.

However, the steady-state inaccuracy of the typical control technique becomes apparent after the power quality oscillations’ settling period. The response is sluggish, and the transient peak is above the maximum limit, reflecting the poor control operation during transient and steady-state operations of the WECS. So, it is clear that the proposed NNPC controller obtained better results than the PI controller.

5.5. DFIG Mechanical Torque

The mechanical torque waveforms of the grid interaction and the generator behaviour with both control schemes are displayed in Figure 37, Figure 38, Figure 39, Figure 40, Figure 41 and Figure 42. In the proposed model of the DFIG with NNPC, a three-phase fault is established to the load side with a 1-s duration (10 s to 11 s). The high torque variations occur in the PI case. The figures show the mechanical and electric torque after the fault condition is maintained in the two cases. Still, there are some variations during the fault condition when using the PI controller. The results obtained using the proposed NNPC controller are, thus, demonstrably superior to those obtained with the PI controller. The results are analysed in the following ways:

In the proposed model of the DFIG with PI control and NNPC systems at 4 m/s of wind speed, as shown in Figure 37, the NNPC system has the DFIG mechanical torque value −1.13665 p.u. to −1.22417 p.u. during the fault condition from 10 s to 11 s. The T_m reached its lowest value at −4.53542 at 16.0096 s before it started gaining its initial value before the fault condition. On the other hand, the PI control system has the DFIG mechanical torque value −1.14833 p.u. to −1.30979 p.u. during the fault condition from 10 s to 11 s. The T_m reached its lowest value at −4.53688 at 16.0791 s before gaining its initial value of −0.489085 Nm at 40.0549 s.

Figure 37. DFIGs mechanical torque analysis, NNPC vs. PI control system at 4 m/s of wind speed.

Figure 37. DFIGs mechanical torque analysis, NNPC vs. PI control system at 4 m/s of wind speed.

At 6 m/s of wind speed, as shown in Figure 38, the NNPC system has the DFIG mechanical torque value −1.64231 p.u. to −1.9963 p.u. during the fault condition from 10 s to 11 s. The T_m has reached its lowest value at −1.32871 at 12.3336 s before it starts gaining its initial value before the fault condition. On the other hand, the PI control system has the DFIG mechanical torque value −1.64427 p.u. to −2.02135 p.u. with the lowest value at −1.31049 at 12.62962 s before settling down to −0.490302 Nm value at 38.6239 s.

Figure 38. DFIGs mechanical torque analysis, NNPC vs. PI control system at 6 m/s of wind speed.

Figure 38. DFIGs mechanical torque analysis, NNPC vs. PI control system at 6 m/s of wind speed.

At 8 m/s of wind speed, as shown in Figure 39, the NNPC system has the DFIG mechanical torque value −1.31998 Nm to −1.20227 Nm during the fault condition from 10 s to 11 s. The T_m has reached the lowest value of −1.396427 at 14.596 s before it starts gaining its initial value before the fault condition. The T_m has settled down to a value of −0.493782 at 42.2085 s. On the other hand, the PI control system has the DFIG mechanical torque value −1.31998 p.u. to −1.23885 p.u. with the lowest value of −1.399205 at 14.1144 s before settling down to −0.5006 Nm value at 41.9974 s.

Figure 39. DFIGs mechanical torque analysis, NNPC vs. PI control system at 8 m/s of wind speed.

Figure 39. DFIGs mechanical torque analysis, NNPC vs. PI control system at 8 m/s of wind speed.

At 10 m/s of wind speed, as shown in Figure 40, the NNPC system has the DFIG mechanical torque value −1.17378 Nm to −1.13428 Nm during the fault condition from 10 s to 11 s. The T_m reached the lowest value of −1.216427 at 11.596 s before gaining close to its initial value before the fault condition. The T_m has settled down to a value of −0.488372 at 42.3344 s. On the other hand, the PI control system has the DFIG mechanical torque value −0.994307 p.u. to −1.17378 p.u. during the fault condition before it settles down to −0.489018 Nm value at 42.4287 s.

Figure 40. DFIGs mechanical torque analysis, NNPC vs. PI control system at 10 m/s of wind speed.

Figure 40. DFIGs mechanical torque analysis, NNPC vs. PI control system at 10 m/s of wind speed.

At 12 m/s of wind speed, as shown in Figure 41, the NNPC system has the DFIG mechanical torque value −0.722156 Nm to −0.811794 Nm during the fault condition from 10 s to 11 s. The T_m has reached the lowest value of −0.96427 at 14.696 s before it starts gaining its initial value before the fault condition. The T_m has settled down to −0.493782 at 29.2085 s before reaching a maximum value of −0.281567 at 23.2519 s. On the other hand, the PI control system has the DFIG mechanical torque value −0.734289 p.u. to −0.850808 p.u. with the lowest value of −1.98205 at 15.1144 s before it settles down to −0.492191 Nm value at 29.8828 s.

Figure 41. DFIGs mechanical torque analysis, NNPC vs. PI control system at 12 m/s of wind speed.

Figure 41. DFIGs mechanical torque analysis, NNPC vs. PI control system at 12 m/s of wind speed.

At 20 m/s of wind speed, as shown in Figure 42, the NNPC system has the DFIG mechanical torque value −0.274929 Nm to −0.325369 Nm during the fault condition from 10 s to 11 s. The T_m reached the lowest value of −0.356427 at 11.596 s before gaining close to its initial value before the fault condition. The T_m has settled down to a value of −0.308824 at 12.408 s. On the other hand, the PI control system has the DFIG mechanical torque value −0.274929 p.u. to −0.323259 p.u. during the fault condition before it settles down to −0.290463 Nm value at 25.8861 s.

Figure 42. DFIGs mechanical torque analysis, NNPC vs. PI control system at 20 m/s of wind speed.

Figure 42. DFIGs mechanical torque analysis, NNPC vs. PI control system at 20 m/s of wind speed.

5.6. DFIG Electrical Torque

Figure 43, Figure 44, Figure 45, Figure 46, Figure 47 and Figure 48 show the electrical torque waveforms of the grid interaction and the generator behaviour with both control schemes. In the proposed model of the DFIG with NNPC, a three-phase fault is established to the load side with a 1-s duration (10 s to 11 s). The high torque variations occur during the fault condition when using the PI controller. The results obtained using the proposed NNPC controller are, thus, demonstrably superior to those obtained with the PI controller. The results are analysed in the following ways:

In the proposed model of the DFIG with PI and NNPC systems at 4 m/s of wind speed, as shown in Figure 43, the NNPC control system has the DFIG electrical torque value −2.42183 Nm to −0.839686 Nm during the fault condition from 10 s to 11 s. The simulation results saw the amplitude variations of T_m from a lowest value of −3.3046 at 11.01 s to a highest value of +5.08427 at 11.0654 s before it started gaining to its initial value of −0.350213 Nm before the fault condition. On the other hand, the PI control system has the DFIG electrical torque value −2.25575 Nm to −0.839686 Nm with the lowest value of −8.89956 p.u. at 10.03506 s before it starts gaining to its initial value before the fault condition.

Figure 43. DFIGs electrical torque analysis, NNPC vs. PI control system at 4 m/s of wind speed.

Figure 43. DFIGs electrical torque analysis, NNPC vs. PI control system at 4 m/s of wind speed.

At 6 m/s of wind speed, as shown in Figure 44, the NNPC system has the DFIG electrical torque value −0.611036 Nm to −0.937531 Nm during the fault condition from 10 s to 11 s. The simulation results saw the amplitude variations of T_m from the lowest value of −3.4346 at 11.051 s to the highest value of +5.15692 at 11.086 s before it started gaining to its initial value of +0.450213 Nm before the fault condition. On the other hand, the PI control system has the DFIG electrical torque value −0.792711 Nm to +0.418257 Nm with the lowest value of −2.89956 p.u. at 10.1356 s before it starts gaining to its initial value before the fault condition.

Figure 44. DFIGs electrical torque analysis, NNPC vs. PI control system at 6 m/s of wind speed.

Figure 44. DFIGs electrical torque analysis, NNPC vs. PI control system at 6 m/s of wind speed.

At 8 m/s of wind speed, as shown in Figure 45, the NNPC system has the DFIG electrical torque value −0.594338 Nm to +0.486752 Nm during the fault condition from 10 s to 11 s. The simulation results saw the amplitude variations of T_m from the lowest value of −3.54666 at 11.0175 s to the highest value of +5.11732 at 11.066 s before it started gaining to its initial value of +0.505213 Nm before the fault condition. On the other hand, the PI control system has the DFIG electrical torque value −0.542927 Nm to +0.431368 Nm with the lowest value of −2.85156 p.u. at 10.156 s before it starts gaining to its initial value before the fault condition.

Figure 45. DFIGs electrical torque analysis, NNPC vs. PI control system at 8 m/s of wind speed.

Figure 45. DFIGs electrical torque analysis, NNPC vs. PI control system at 8 m/s of wind speed.

At 10 m/s of wind speed, as shown in Figure 46, the NNPC system has the DFIG electrical torque value −0.494338 Nm to −0.840953 Nm during the fault condition from 10 s to 11 s. The simulation results saw the amplitude variations of T_m from the lowest value of −3.58566 at 11.0575 s to the highest value of +5.10377 at 11.0866 s before it started gaining to its initial value of +0.515213 Nm before the fault condition. On the other hand, the PI control system has the DFIG electrical torque value −0.497591 Nm to −0.411752 Nm with the lowest value of −2.6501 Nm at 10.156 s before it starts gaining to its initial value before the fault condition.

Figure 46. DFIGs electrical torque analysis, NNPC vs. PI control system at 10 m/s of wind speed.

Figure 46. DFIGs electrical torque analysis, NNPC vs. PI control system at 10 m/s of wind speed.

At 12 m/s of wind speed, as shown in Figure 47, the NNPC system has the DFIG electrical torque value −1.94704 Nm to +0.906327 Nm during the fault condition from 10 s to 11 s. The simulation results saw the amplitude variations of T_m from the lowest value of −3.49097 at 11.018 s to the highest value of +5.13387 at 11.0864 s before it started gaining to its initial value of +0.618213 Nm before the fault condition. On the other hand, the PI control system has the DFIG electrical torque value −1.70551 Nm to −0.239733 Nm with the lowest value of −2.65156 p.u. at 10.156 s before it starts gaining to its initial value before the fault condition.

Figure 47. DFIGs electrical torque analysis, NNPC vs. PI control system at 12 m/s of wind speed.

Figure 47. DFIGs electrical torque analysis, NNPC vs. PI control system at 12 m/s of wind speed.

At 20 m/s of wind speed, as shown in Figure 48, the NNPC system has the DFIG electrical torque value −0.774813 Nm to −1.80778 Nm during the fault condition from 10 s to 11 s. The simulation results saw the amplitude variations of T_m from the lowest value of −3.38156 at 11.0505 s to the highest value of +5.14662 at 11.0657 s before it started gaining to its initial value of +0.635213 Nm before the fault condition. On the other hand, the PI control system has the DFIG electrical torque value −1.33088 Nm to −0.497847 Nm with the lowest value of −2.76501 Nm at 10.101 s, before it starts gaining to its initial value before the fault condition.

The figures show the electric torque after the fault condition is maintained in the two cases. The results obtained using the proposed NNPC controller are, thus, demonstrably superior to those obtained with the PI controller.

Figure 48. DFIGs electrical torque analysis, NNPC vs. PI control system at 20 m/s of wind speed.

Figure 48. DFIGs electrical torque analysis, NNPC vs. PI control system at 20 m/s of wind speed.

6. Discussions

It is more difficult and time-consuming for complex and large-scale systems, such as the DFIG-based WECS to obtain optimal K_p and K_i gains values using empirical approaches and trial-and-error-based procedures in the PI-controlled framework. Therefore, a promising approach is to frame the choice of the K_p and K_i gains as an optimisation problem. This paper reviewed comprehensive NN methodologies and established that, with the help of sophisticated metaheuristics, a control issue of this nature, which can be nonlinear, non-smooth, or even non-convex, can be successfully resolved. The results obtained as a comparison between the suggested NNPC methodology, and the traditional PI control strategy are summarised in

Table 8. Summary of the results obtained from Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28, Figure 29, Figure 30, Figure 31, Figure 32, Figure 33, Figure 34, Figure 35, Figure 36, Figure 37, Figure 38, Figure 39, Figure 40, Figure 41, Figure 42, Figure 43, Figure 44, Figure 45, Figure 46, Figure 47 and Figure 48.

Wind Speed	Parameters	Conventional Control System PI		Proposed NNPC Control System
		Measured parameter value at the time of the fault’s occurrence at 10 s	Measured parameter value at the time of the fault’s clearance at 11 s	Measured parameter value at the time of the fault’s occurrence at 10 s	Measured parameter value at the time of the fault’s clearance at 11 s
4 m/s	Active power P (p.u.)	−0.337643	0.995336	0.587395	−0.38125
6 m/s	Active power P (p.u.)	0.687793	0.992803	−0.183274	0.353574
8 m/s	Active power P (p.u.)	0.583642	0.994375	0.583642	−0.0402709
10 m/s	Active power P (p.u.)	0.364014	0.926663	0.364014	−0.188284
12 m/s	Active power P (p.u.)	0.0958262	0.999815	0.48102	0.352744
4 m/s	Reactive power P (p.u.)	0.50081	1.66219	0.50081	−0.120725
6 m/s	Reactive power P (p.u.)	0.5000003	1.65292	0.5000003	−0.127539
8 m/s	Reactive power P (p.u.)	0.500309	1.5926	0.500309	−0.230327
10 m/s	Reactive power P (p.u.)	0.498499	1.63642	0.498499	−0.433483
12 m/s	Reactive power P (p.u.)	0.497576	1.65575	0.497576	−0.22814
20 m/s	Reactive power P (p.u.)	0.499581	1.56047	0.499581	−0.303208
4 m/s	DC bus voltage Vdc	1000.64	9940.41	1000.64	2404.61
6 m/s	DC bus voltage Vdc	1001.07	11084.8	1001.07	3010.06
8 m/s	DC bus voltage Vdc	1006.08	10060.5	1006.08	1018.57
10 m/s	DC bus voltage Vdc	1000.5	9178.28	1000.5	1998.56
12 m/s	DC bus voltage Vdc	664.164	7972.24	1000.12	1680.33
20 m/s	DC bus voltage Vdc	999.895	8995.19	999.885	1448.05
4 m/s	Grid side d-q axis d-current in amps	−0.0931398	−0.133235	−0.0931398	−0.117086
6 m/s	Grid side d-q axis d-current in amps	−0.205465	−0.147967	−0.205465	−0.283805
8 m/s	Grid side d-q axis d-current in amps	−0.1279	−0.124894	−0.1279	−0.124872
10 m/s	Grid side d-q axis d-current in amps	−0.0370604	−0.13295	−0.0370604	−0.119728
4 m/s	Grid side d-q axis q-current in amps	−0.00199687	0.474912	−0.00199687	0.463976
6 m/s	Grid side d-q axis q-current in amps	0.00445024	0.484423	−0.00560673	0.459598
8 m/s	Grid side d-q axis q-current in amps	−0.00241283	0.483977	−0.00241283	0.449759
10 m/s	Grid side d-q axis q-current in amps	−0.000171633	0.883977	0.00123818	0.460542
4 m/s	Mechanical torque in (p.u.)	−1.14833	−1.30979	−1.13665	−1.22417
6 m/s	Mechanical torque in (p.u.)	−1.64427	−2.02135	−1.64231	−1.9963
8 m/s	Mechanical torque in (p.u.)	−1.31998	−1.23885	−1.31998	−1.20227
10 m/s	Mechanical torque in (p.u.)	−0.994307	−1.17378	−0.994307	−1.13428
12 m/s	Mechanical torque in (p.u.)	−0.734289	−0.850808	−0.722156	−0.811794
20 m/s	Mechanical torque in (p.u.)	−0.274929	−0.323259	−0.274929	−0.325369
4 m/s	Electrical torque in (p.u.)	−2.25575	−0.184678	−2.42183	−0.839686
6 m/s	Electrical torque in (p.u.)	−0.792711	0.418257	−0.611036	−0.937531
8 m/s	Electrical torque in (p.u.)	−0.542927	0.431368	−0.594338	0.486752
10 m/s	Electrical torque in (p.u.)	−0.497591	−0.411752	−0.497591	−0.840953
12 m/s	Electrical torque in (p.u.)	−1.70551	−0.239733	−1.94704	0.906327
20 m/s	Electrical torque in (p.u.)	−1.33088	−0.497847	−0.774813	−1.80778

. The measured parameter data demonstrate that the NNPC method exhibits less variance in the estimated data before and after the fault occurrence than the PI control strategy. To follow is a detailed analysis and discussion of several of the DFIG parameters.

The suggested ANN control approach achieves better overall active and reactive power results because it settles faster and causes less overshoot during transient operation. Additionally, it produces a better result than the standard PI control method since it dampens oscillations more quickly and has less ripple content. A shorter time may be needed during steady-state operation to obtain the reference reactive power level according to the appropriate power quality behaviour. The waveform’s ripple is also less pronounced than it would be otherwise. The traditional control technique has poor settling time and a steady-state error beyond the settling period. Weak control performance during the transient and steady-state operations of the WECS is indicated by the delayed reaction and transient peak, both above the maximum limit.

Before the fault state appeared, the DC bus voltage in the NNPC system was 1001.07 volts. The DC bus voltage did, however, experience a maximum variance of 3442.45 volts during the fault condition between 10 and 11 s, with fewer waves, until attaining a steady-state condition of 1001.06 DC volts at 11.2535 s. On the other hand, the PI control system had a greater DC bus voltage over a 1-s fault incidence period, ranging from 8000 to 11,084.8 volts. The PI control spiked the DC bus voltage, with a delayed response stabilising at 998.07 volts after 12.805 s.

The DFIG mechanical torque T_m and electrical torque T_e values in the NNPC system vary by 0.5 p.u. between 10 and 11 s of the fault situation. Unlike the NNPC system, the PI control system experiences DFIG mechanical torque and electrical torque value variations between 0.5 and 1.0 p.u. under faulty circumstances before stabilising for a more extended period.

7. Conclusions

This paper elaborates on an ANN-based control solution for WECS’s connected to the grid to improve the system performance under different operating criteria, mainly during a transient fault condition. The results show that the suggested control technique enhances the WECS’s functionality when connected to a grid. Regarding power quality, an ANN-based control produces fewer disturbances, strengthening the power system’s effectiveness. Additionally, it responds to transients well and lessens ripple-related distortion. The error also reduces the time needed to settle and the time required to reach a steady state compared to the conventional PI control system. According to our analysis, choosing the appropriate training dataset is essential for enhancing ANN-based control results and lowering the computational load. This paper advances the use of machine learning control algorithms in the renewable energy sector, where there are several parametric uncertainties.

The suggested simulation model has shown that neural network predictive control (NNPC) improves the performance of grid-connected wind energy systems. According to the findings of the fault conditioning experiment, the suggested control method outperforms the PI controller in terms of active and reactive power, mechanical and electric torque, and DC bus voltage. In two instances, the active and reactive power is unaffected during the fault condition, except for fluctuations when a PI-type controller operates. Regarding performance, the proposed NNPC controller fared better than the PI controller. In two instances, the mechanical and electric torque is kept constant at the same level as before the problem. However, there are fluctuations when employing a PI controller.

Given that the DC bus voltage in the PI example is between 9000 and 10,000 volts during a fault situation but is only between 3001 and 3500 volts in the NNPC controller, it is evident that the high DC bus voltage is occurring in the PI example. This study has demonstrated that NNPC is a more reliable and efficient control mechanism for wind energy systems than the PI controller. It will be a desirable choice for wind energy system owners and operators wanting to increase their system’s efficiency.